The Garduino Instructable
is probably your best resource for starting this project. It has tons of great insights that will help you get started with your own arduino controlled garden. He has also put together a website with more pictures and a kit that you can get, but I chose to build this project with my own parts.
When you get started you'll want to get some plants and a place to plant them. I recommend a local gardening store where possible. You'll pick up some healthy plants there and probably a few good tips on how to care for them. I picked up basil and mint, a couple plants I'd find useful to have for cooking. I also got an 8" x 18" planter with a matching dish to catch water. You can certainly go out and use tubs or custom pots, just choose what's right for you and your plants. Also, pick something that will look nice around your house if that's important to you.
The first thing that is different about my project is that I was building an indoor garden. My apartment doesn't have a lot of light from any of the windows, nor does any good light fall on the patio. This changed a lot of the parameters for my garden. For one, I didn't need a light or temperature sensor, something I discovered after the fact, as my light will be constant from the fluorescent bulb and my temperature inside the apartment is pretty stable.
I also learned that whether you choose to keep your plants inside or outside you should be aware of bugs. My first plants died because of spider mites
, something I hadn't even thought of when starting this project. I found the solution was actually pretty easy, involving a spray bottle, a tiny bit of soap and water. It's a much cleaner solution, especially if you plan to eat your plants, and doesn't hurt the environment either.